On a proof of Shelah by Hajnal Andréka
This is Part I of the presentation of a talk given on September 27, 2013 at the Logic and Philoso... more This is Part I of the presentation of a talk given on September 27, 2013 at the Logic and Philosophy of Mathematics seminar of ELTE University, Budapest. We present a concrete mathematical realization for the Leibnizian relationist concept of time and space, via a logical analysis of exploring time and space experimentally. We start out from ideas in James Ax’s 1978 paper entitled “The elementary foundations of spacetime”.
Transactions of the American Mathematical Society, 1988
... A STONE TYPE REPRESENTATION THEOREM FOR ALGEBRAS OF RELATIONS OF HIGHERRANK ... every Boolean... more ... A STONE TYPE REPRESENTATION THEOREM FOR ALGEBRAS OF RELATIONS OF HIGHERRANK ... every Boolean algebra with operators 21 can be embedded into an atomic one such that all the equations valid in 21, and in which "—" does not occur, continue to hold in the ...
Lecture Notes in Computer Science, 1983
Without Abstract
Proceedings of the American Mathematical Society, 1987
… dedicated to Johan van Benthem on …, 1999
Logical analysis of special relativity theory Hajnal AndrÈeka, Judit X. MadarÈasz, and IstvÈan NÈ... more Logical analysis of special relativity theory Hajnal AndrÈeka, Judit X. MadarÈasz, and IstvÈan NÈemeti* 1 Introduction ... Assume that trm ( fi ) = trm ( ph ) for some m,fi e Obs,ph e Ph in a model of Specrel . Then trk ( fi ) = t and vk ( ph ) = 1by Ax2,AxE . Thus trk ( fi ) φ= trk ( ph ). ...
Annals of Pure and Applied Logic, 1997
We study algebras whose elements are relations, and the operations are natural "manipulations" of... more We study algebras whose elements are relations, and the operations are natural "manipulations" of relations. This area goes back to I40 years ago to works of De Morgan, Pence, Schroder (who expanded the Boolean tradition with extra operators to handle algebras of binary relations).
... between com-puting, AI, foundations of science, emergence, new cosmology, black hole physics ... more ... between com-puting, AI, foundations of science, emergence, new cosmology, black hole physics are highlighted. Because of hypercomputation and unconventional approaches to computa-tion, new interconnections arose recently between computability theory, physics, and ...
Algebra Universalis, 1988
We show that the class of all relativized (in the usual sense) relation algebras is not closed un... more We show that the class of all relativized (in the usual sense) relation algebras is not closed under taking subalgebras. Moreover, we show that there is a complete and atomic subalgebra which is not in the original class (relation composition is not completely additive in it). These results are in contrast with results in Maddux [82] and in Henkin-Resek [75].
Algebra Universalis, 1995
We solve a problem of J6nsson by showing that the class Y/of (isomorphs of) algebras of binary re... more We solve a problem of J6nsson by showing that the class Y/of (isomorphs of) algebras of binary relations, under the operations of relative product, conversion, and intersection, and with the identity element as a distinguished constant, is not axiomatizable by a set of equations. We also show that the set of equations valid in ~ is decidable, and in fact the set of equations true in the class of all positive algebras of relations is decidable.
Algebra Universalis, 1991
ABSTRACT
Algebra Universalis, 1991
Let R(n, u, I) denote the class of all algebras isomorphic to ones whose elements are binary rela... more Let R(n, u, I) denote the class of all algebras isomorphic to ones whose elements are binary relations and whose operations are union, intersection, and relation composition (or relative product) of relations. We prove that R(w, c~, l) is not a variety and is not finitely axiomatizable. Let DLOS denote the class of all structures (A, v, ^, o) where (A, v, ^ ) is a distributive lattice, (A, o) is a semigroup and o is additive w.r.t.v. We prove that DLOS is the variety generated by R(u, n, [), and moreover, if (A, v, A, o) e DLOS then it is representable whenever we disregard one of its operations.
Algebra Universalis, 1985
In Pasztor [4] the notion of relative epi was introduced in order to characterize surjections of ... more In Pasztor [4] the notion of relative epi was introduced in order to characterize surjections of certain concrete categories. Our main motivation in trying to characterize surjections in category theoretical terms is that there is a kind of abstract model theory (see e.g. Andrrka, Nrmeti [1] and Nrmeti, Sain [3]) whose applications and further development need this characterization.
Journal of logic and …, Jan 1, 2002
The paper is a theoretical study of a generalization of the lexicographic rule for combining orde... more The paper is a theoretical study of a generalization of the lexicographic rule for combining ordering relations. We define the concept of priority operator: a priority operator maps a family of relations to a single relation which represents their lexicographic combination according to a certain priority on the family of relations. We present four kinds of results.
Notre Dame Journal of Formal Logic, 1994
There are eighteen isomorphism types of finite relation algebras with eight or fewer elements, an... more There are eighteen isomorphism types of finite relation algebras with eight or fewer elements, and all of them are representable. We determine all the cardinalities of sets on which these algebras have representations.
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On a proof of Shelah by Hajnal Andréka